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A television station runs a telephone survey to determine how many persons in its primary viewing area have watched three recent special programs, which wecall a, b, and c. Of the 1000 persons surveyed, the results are:
221 have seen at least a; 209 have seen at least b; 112 have seen at least c; 197 have seen at least two of the programs; 45 have seen all three; 62 have seen at least a and c; the number having seen at least a and b is twice as large as the number who have seen at least b and c.
% file
npr02_16.m % Data for
[link] minvec3
DV = [A|Ac; A; B; C; (A&B)|(A&C)|(B&C); A&B&C; A&C; (A&B)-2*(B&C)];DP = [ 1 0.221 0.209 0.112 0.197 0.045 0.062 0];TV = [A|B|C; (A&Bc&Cc)|(Ac&B&Cc)|(Ac&Bc&C)];npr02_16
Variables are A, B, C, Ac, Bc, CcThey may be renamed, if desired.
Call for mincalcmincalc
Data vectors are linearly independentComputable target probabilities
1.0000 0.30002.0000 0.1030
The number of minterms is 8The number of available minterms is 8
Available minterm probabilities are in vector pmaTo view available minterm probabilities, call for PMA An automobile safety inspection station found that in 1000 cars tested:
% file
npr02_17.m % Data for
[link] % A = alignment; B = brake work; C = headlight
minvec3DV = [A|Ac; A&B&C; (A&B)|(A&C)|(B&C); B&C; A ];DP = [ 1 0.100 0.325 0.125 0.550];TV = [A&Bc&Cc; Ac&(~(B&C))];disp('Call for mincalc')
npr02_17Variables are A, B, C, Ac, Bc, Cc
They may be renamed, if desired.Call for mincalc
mincalcData vectors are linearly independent
Computable target probabilities1.0000 0.2500
2.0000 0.4250The number of minterms is 8
The number of available minterms is 3Available minterm probabilities are in vector pma
To view available minterm probabilities, call for PMA Suppose .
Determine , , and , if possible.
Repeat the problem with the additional data and .
% file
npr02_18.m % Date for
[link] minvec3
DV = [A|Ac; A&(B|C); Ac; Ac&Bc&Cc];DP = [ 1 0.3 0.6 0.1];TV = [B|C; (((A&B)|(Ac&Bc))&Cc)|(A&C); Ac&(B|Cc)];disp('Call for mincalc')
% Modification% DV = [DV; Ac&B&C; Ac&B];% DP = [DP 0.2 0.3];npr02_18
Variables are A, B, C, Ac, Bc, CcThey may be renamed, if desired.
Call for mincalcmincalc
Data vectors are linearly independentComputable target probabilities
1.0000 0.80002.0000 0.4000
The number of minterms is 8The number of available minterms is 2
Available minterm probabilities are in vector pmaTo view available minterm probabilities, call for PMA
DV = [DV; Ac&B&C; Ac&B]; % Modified dataDP = [DP 0.2 0.3];mincalc % New calculation
Data vectors are linearly independentComputable target probabilities
1.0000 0.80002.0000 0.4000
3.0000 0.4000The number of minterms is 8
The number of available minterms is 5Available minterm probabilities are in vector pma
To view available minterm probabilities, call for PMA 
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